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c6b6b8f Merge dashpay#830: Rip out non-endomorphism code + dependencies c582aba Consistency improvements to the comments 63c6b71 Reorder comments/function around scalar_split_lambda 2edc514 WNAF of lambda_split output has max size 129 4232e5b Rip out non-endomorphism code ebad841 Check correctness of lambda split without -DVERIFY fe7fc1f Make lambda constant accessible 9d2f2b4 Add tests to exercise lambda split near bounds 9aca2f7 Add secp256k1_split_lambda_verify acab934 Detailed comments for secp256k1_scalar_split_lambda 76ed922 Increase precision of g1 and g2 6173839 Switch to our own memcmp function 63150ab Merge dashpay#827: Rename testrand functions to have test in name c5257ae Merge dashpay#821: travis: Explicitly set --with-valgrind bb1f542 Merge dashpay#818: Add static assertion that uint32_t is unsigned int or wider a45c1fa Rename testrand functions to have test in name 5006895 Merge dashpay#808: Exhaustive test improvements + exhaustive schnorrsig tests 4eecb4d travis: VALGRIND->RUN_VALGRIND to avoid confusion with WITH_VALGRIND 66a765c travis: Explicitly set --with-valgrind d7838ba Merge dashpay#813: Enable configuring Valgrind support 7ceb0b7 Merge dashpay#819: Enable -Wundef warning 8b7dcdd Add exhaustive test for extrakeys and schnorrsig 08d7d89 Make pubkey parsing test whether points are in the correct subgroup 87af00b Abstract out challenge computation in schnorrsig 63e1b2a Disable output buffering in tests_exhaustive.c 39f67dd Support splitting exhaustive tests across cores e99b26f Give exhaustive_tests count and seed cmdline inputs 49e6630 refactor: move RNG seeding to testrand b110c10 Change exhaustive test groups so they have a point with X=1 cec7b18 Select exhaustive lambda in function of order 78f6cdf Make the curve B constant a secp256k1_fe d7f39ae Delete gej_is_valid_var: unused outside tests 8bcd78c Make secp256k1_scalar_b32 detect overflow in scalar_low c498366 Move exhaustive tests for recovery to module be31791 Make group order purely compile-time in exhaustive tests e73ff30 Enable -Wundef warning c0041b5 Add static assertion that uint32_t is unsigned int or wider 4ad408f Merge dashpay#782: Check if variable=yes instead of if var is set in travis.sh 412bf87 configure: Allow specifying --with[out]-valgrind explicitly 34debf7 Modify .travis.yml to explictly pass no in env vars instead of setting to nothing a0e99fc Merge dashpay#814: tests: Initialize random group elements fully 5738e86 tests: Initialize random group elements fully c9939ba Merge dashpay#812: travis: run bench_schnorrsig a51f2af travis: run bench_schnorrsig ef37761 Change travis.sh to check if variables are equal to yes instead of not-empty. Before this, setting `VALGRIND=wat` was considered as true, and to make it evaluate as false you had to unset the variable `VALGRIND=` but not it checks if `VALGRIND=yes` and if it's not `yes` then it's evaluated to false git-subtree-dir: src/secp256k1 git-subtree-split: c6b6b8f
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,129 @@ | ||
| # Define field size and field | ||
| P = 2^256 - 2^32 - 977 | ||
| F = GF(P) | ||
| BETA = F(0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee) | ||
|
|
||
| assert(BETA != F(1) and BETA^3 == F(1)) | ||
|
|
||
| orders_done = set() | ||
| results = {} | ||
| first = True | ||
| for b in range(1, P): | ||
| # There are only 6 curves (up to isomorphism) of the form y^2=x^3+B. Stop once we have tried all. | ||
| if len(orders_done) == 6: | ||
| break | ||
|
|
||
| E = EllipticCurve(F, [0, b]) | ||
| print("Analyzing curve y^2 = x^3 + %i" % b) | ||
| n = E.order() | ||
| # Skip curves with an order we've already tried | ||
| if n in orders_done: | ||
| print("- Isomorphic to earlier curve") | ||
| continue | ||
| orders_done.add(n) | ||
| # Skip curves isomorphic to the real secp256k1 | ||
| if n.is_pseudoprime(): | ||
| print(" - Isomorphic to secp256k1") | ||
| continue | ||
|
|
||
| print("- Finding subgroups") | ||
|
|
||
| # Find what prime subgroups exist | ||
| for f, _ in n.factor(): | ||
| print("- Analyzing subgroup of order %i" % f) | ||
| # Skip subgroups of order >1000 | ||
| if f < 4 or f > 1000: | ||
| print(" - Bad size") | ||
| continue | ||
|
|
||
| # Iterate over X coordinates until we find one that is on the curve, has order f, | ||
| # and for which curve isomorphism exists that maps it to X coordinate 1. | ||
| for x in range(1, P): | ||
| # Skip X coordinates not on the curve, and construct the full point otherwise. | ||
| if not E.is_x_coord(x): | ||
| continue | ||
| G = E.lift_x(F(x)) | ||
|
|
||
| print(" - Analyzing (multiples of) point with X=%i" % x) | ||
|
|
||
| # Skip points whose order is not a multiple of f. Project the point to have | ||
| # order f otherwise. | ||
| if (G.order() % f): | ||
| print(" - Bad order") | ||
| continue | ||
| G = G * (G.order() // f) | ||
|
|
||
| # Find lambda for endomorphism. Skip if none can be found. | ||
| lam = None | ||
| for l in Integers(f)(1).nth_root(3, all=True): | ||
| if int(l)*G == E(BETA*G[0], G[1]): | ||
| lam = int(l) | ||
| break | ||
| if lam is None: | ||
| print(" - No endomorphism for this subgroup") | ||
| break | ||
|
|
||
| # Now look for an isomorphism of the curve that gives this point an X | ||
| # coordinate equal to 1. | ||
| # If (x,y) is on y^2 = x^3 + b, then (a^2*x, a^3*y) is on y^2 = x^3 + a^6*b. | ||
| # So look for m=a^2=1/x. | ||
| m = F(1)/G[0] | ||
| if not m.is_square(): | ||
| print(" - No curve isomorphism maps it to a point with X=1") | ||
| continue | ||
| a = m.sqrt() | ||
| rb = a^6*b | ||
| RE = EllipticCurve(F, [0, rb]) | ||
|
|
||
| # Use as generator twice the image of G under the above isormorphism. | ||
| # This means that generator*(1/2 mod f) will have X coordinate 1. | ||
| RG = RE(1, a^3*G[1]) * 2 | ||
| # And even Y coordinate. | ||
| if int(RG[1]) % 2: | ||
| RG = -RG | ||
| assert(RG.order() == f) | ||
| assert(lam*RG == RE(BETA*RG[0], RG[1])) | ||
|
|
||
| # We have found curve RE:y^2=x^3+rb with generator RG of order f. Remember it | ||
| results[f] = {"b": rb, "G": RG, "lambda": lam} | ||
| print(" - Found solution") | ||
| break | ||
|
|
||
| print("") | ||
|
|
||
| print("") | ||
| print("") | ||
| print("/* To be put in src/group_impl.h: */") | ||
| first = True | ||
| for f in sorted(results.keys()): | ||
| b = results[f]["b"] | ||
| G = results[f]["G"] | ||
| print("# %s EXHAUSTIVE_TEST_ORDER == %i" % ("if" if first else "elif", f)) | ||
| first = False | ||
| print("static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(") | ||
| print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(G[0]) >> (32 * (7 - i))) & 0xffffffff for i in range(4))) | ||
| print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(G[0]) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8))) | ||
| print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(G[1]) >> (32 * (7 - i))) & 0xffffffff for i in range(4))) | ||
| print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x" % tuple((int(G[1]) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8))) | ||
| print(");") | ||
| print("static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(") | ||
| print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(b) >> (32 * (7 - i))) & 0xffffffff for i in range(4))) | ||
| print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x" % tuple((int(b) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8))) | ||
| print(");") | ||
| print("# else") | ||
| print("# error No known generator for the specified exhaustive test group order.") | ||
| print("# endif") | ||
|
|
||
| print("") | ||
| print("") | ||
| print("/* To be put in src/scalar_impl.h: */") | ||
| first = True | ||
| for f in sorted(results.keys()): | ||
| lam = results[f]["lambda"] | ||
| print("# %s EXHAUSTIVE_TEST_ORDER == %i" % ("if" if first else "elif", f)) | ||
| first = False | ||
| print("# define EXHAUSTIVE_TEST_LAMBDA %i" % lam) | ||
| print("# else") | ||
| print("# error No known lambda for the specified exhaustive test group order.") | ||
| print("# endif") | ||
| print("") |
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